Three-layer Adaptive Back-Propagation Neural Networks(TABPNN) are employed for the demodulation of spread spectrum signals in a multiple-access environment. A configuration employing three-layer adaptive Back-propagation neural networks is put forward for the demodulation of spread-spectrum signals in asynchronous Gaussian channels. The theoretical arguments and practical performance based on the neural networks are analyzed. The results show that whether the resistance to the multiple access interference or the robust to near-far effects, the proposed detector significantly outperforms not only the conventional detector but also the BP neural networks detector and is comparable to the optimum detector.